A Unit Root Test Using a Fourier Series to Approximate Smooth Breaks

We develop a unit-root test based on a simple variant of Gallant's (1981) flexible Fourier form. The test relies on the fact that a series with several smooth structural breaks can often be approximated using the low frequency components of a Fourier expansion. Hence, it is possible to test for a unit root without having to model the precise form of the break. Our unit-root test employing Fourier approximation has good size and power for the types of breaks often used in economic analysis. The appropriate use of the test is illustrated using several interest rate spreads.